Contributions to the theory of magnetorotational instability and waves in a rotating plasma

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary 0, where 0 is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary P. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

MAGNETOHYDRODYNAMIC SIMULATIONS OF RECONNECTION AND PARTICLE ACCELERATION: THREE-DIMENSIONAL EFFECTS

Magnetic fields can change their topology through a process known as magnetic reconnection. This process in not only important for understanding the origin and evolution of the large-scale magnetic field, but is seen as a possibly efficient particle accelerator producing cosmic rays mainly through the first-order Fermi process. In this work we study the properties of particle acceleration inserted in reconnection zones and show that the velocity component parallel to the magnetic field of test particles inserted in magnetohydrodynamic (MHD) domains of reconnection without including kinetic effects, such as pressure anisotropy, the Hall term, or anomalous effects, increases exponentially. Also, the acceleration of the perpendicular component is always possible in such models. We find that within contracting magnetic islands or current sheets the particles accelerate predominantly through the first-order Fermi process, as previously described, while outside the current sheets and islands the particles experience mostly drift acceleration due to magnetic field gradients. Considering two-dimensional MHD models without a guide field, we find that the parallel acceleration stops at some level. This saturation effect is, however, removed in the presence of an out-of-plane guide field or in three-dimensional models. Therefore, we stress the importance of the guide field and fully three-dimensional studies for a complete understanding of the process of particle acceleration in astrophysical reconnection environments.

THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF MAGNETIZED WINDS OF SOLAR-LIKE STARS

By means of self-consistent three-dimensional magnetohydrodynamics (MHD) numerical simulations, we analyze magnetized solar-like stellar winds and their dependence on the plasma-beta parameter (the ratio between thermal and magnetic energy densities). This is the first study to perform such analysis solving the fully ideal three-dimensional MHD equations. We adopt in our simulations a heating parameter described by gamma, which is responsible for the thermal acceleration of the wind. We analyze winds with polar magnetic field intensities ranging from 1 to 20 G. We show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. Higher magnetic field intensities lead to faster and hotter winds. For the maximum magnetic intensity simulated of 20 G and solar coronal base density, the wind velocity reaches values of similar to 1000 km s(-1) at r similar to 20r(0) and a maximum temperature of similar to 6 x 10(6) K at r similar to 6r(0). The increase of the field intensity generates a larger ""dead zone"" in the wind, i.e., the closed loops that inhibit matter to escape from latitudes lower than similar to 45 degrees extend farther away from the star. The Lorentz force leads naturally to a latitude-dependent wind. We show that by increasing the density and maintaining B(0) = 20 G the system recover back to slower and cooler winds. For a fixed gamma, we show that the key parameter in determining the wind velocity profile is the beta-parameter at the coronal base. Therefore, there is a group of magnetized flows that would present the same terminal velocity despite its thermal and magnetic energy densities, as long as the plasma-beta parameter is the same. This degeneracy, however, can be removed if we compare other physical parameters of the wind, such as the mass-loss rate. We analyze the influence of gamma in our results and we show that it is also important in determining the wind structure.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS. II. THE EFFECTS OF A TILTED MAGNETOSPHERE AND PLANETARY INTERACTIONS

Based on our previous work, we investigate here the effects on the wind and magnetospheric structures of weak-lined T Tauri stars due to a misalignment between the axis of rotation of the star and its magnetic dipole moment vector. In such a configuration, the system loses the axisymmetry presented in the aligned case, requiring a fully three-dimensional (3D) approach. We perform 3D numerical magnetohydrodynamic simulations of stellar winds and study the effects caused by different model parameters, namely the misalignment angle theta(t), the stellar period of rotation, the plasma-beta, and the heating index.. Our simulations take into account the interplay between the wind and the stellar magnetic field during the time evolution. The system reaches a periodic behavior with the same rotational period of the star. We show that the magnetic field lines present an oscillatory pattern. Furthermore, we obtain that by increasing theta(t), the wind velocity increases, especially in the case of strong magnetic field and relatively rapid stellar rotation. Our 3D, time-dependent wind models allow us to study the interaction of a magnetized wind with a magnetized extrasolar planet. Such interaction gives rise to reconnection, generating electrons that propagate along the planet`s magnetic field lines and produce electron cyclotron radiation at radio wavelengths. The power released in the interaction depends on the planet`s magnetic field intensity, its orbital radius, and on the stellar wind local characteristics. We find that a close-in Jupiter-like planet orbiting at 0.05 AU presents a radio power that is similar to 5 orders of magnitude larger than the one observed in Jupiter, which suggests that the stellar wind from a young star has the potential to generate strong planetary radio emission that could be detected in the near future with LOFAR. This radio power varies according to the phase of rotation of the star. For three selected simulations, we find a variation of the radio power of a factor 1.3-3.7, depending on theta(t). Moreover, we extend the investigation done in Vidotto et al. and analyze whether winds from misaligned stellar magnetospheres could cause a significant effect on planetary migration. Compared to the aligned case, we show that the timescale tau(w) for an appreciable radial motion of the planet is shorter for larger misalignment angles. While for the aligned case tau(w) similar or equal to 100 Myr, for a stellar magnetosphere tilted by theta(t) = 30 degrees, tau(w) ranges from similar to 40 to 70 Myr for a planet located at a radius of 0.05 AU. Further reduction on tau(w) might occur for even larger misalignment angles and/or different wind parameters.

PRECESSING JETS AND X-RAY BUBBLES FROM NGC 1275 (3C 84) IN THE PERSEUS GALAXY CLUSTER: A VIEW FROM THREE-DIMENSIONAL NUMERICAL SIMULATIONS

The Perseus galaxy cluster is known to present multiple and misaligned pairs of cavities seen in X-rays, as well as twisted kiloparsec-scale jets at radio wavelengths; both morphologies suggest that the active galactic nucleus (AGN) jet is subject to precession. In this work, we performed three-dimensional hydrodynamical simulations of the interaction between a precessing AGN jet and the warm intracluster medium plasma, whose dynamics are coupled to a Navarro-Frenk-White dark matter gravitational potential. The AGN jet inflates cavities that become buoyantly unstable and rise up out of the cluster core. We found that under certain circumstances precession can originate multiple pairs of bubbles. For the physical conditions in the Perseus cluster, multiple pairs of bubbles are obtained for a jet precession opening angle >40 degrees acting for at least three precession periods, reproducing both radio and X-ray maps well. Based on such conditions, assuming that the Bardeen-Peterson effect is dominant, we studied the evolution of the precession opening angle of this system. We were able to constrain the ratio between the accretion disk and the black hole angular momenta as 0.7-1.4. We were also able to constrain the present precession angle to 30 degrees-40 degrees, as well as the approximate age of the inflated bubbles to 100-150 Myr.

Placental Volumes Measured by 3-Dimensional Ultrasonography in Normal Pregnancies From 12 to 40 Weeks` Gestation

Objective. The purpose of this study was to construct nomograms of placental volumes according to gestational age and estimated fetal weight. Methods. From March to November 2007, placental volumes were prospectively measured by ultrasonography in 295 normal pregnancies from 12 to 40 weeks` gestation and correlated with gestational age and estimated fetal weight. Inclusion criteria were healthy women, singleton pregnancies with normal fetal morphologic characteristics on ultrasonography, and confirmed gestational age by first-trimester ultrasonography. Results. The mean placental volume ranged from 83 cm(3) at 12 weeks to 427.7 cm(3) at 40 weeks. Linear regression yielded the following formula for the expected placental volumes (ePV) according to gestational age (GA): ePV` (cm(3)) = -64.68 + 12.31 x GA (r = 0.572; P < .001). Placental volumes also varied according to estimated fetal weight (EFW), and the following mathematical equation was also obtained by linear regression: ePV = 94.19 + 0.09 x EFW (r = 0.505; P < 0.001). Conclusions. Nomograms of placental volumes according to gestational age and estimated fetal weight were constructed, generating reference values.

Predictable drill-free screw positioning with a graduated 3-dimensional radiographic-surgical guide: A preliminary report

Introduction: Mini-implants are placed in restricted sites, requiring an accurate surgical technique. However, no systematic study has quantified technique accuracy to reliably predict the surgical risks. Therefore, a graduated 3-dimensional radiographic-surgical guide (G-RSG) was proposed, and its inaccuracy and risk index (RI) were estimated. Methods: The sample consisted of 6 subjects (4 male, 2 female), who used mini-implant anchorage. Ten drill-free screws (DFS) were placed by using the G-RSG. The central point of the mesiodistal septum width (SW) was the selected implant site on the presurgical radiograph. The distances between DFS and the adjacent teeth (5-DFS and 6-DFS) were measured to evaluate screw centralization and inaccuracy degree (ID). These distances were statistically compared by independent t tests, and inaccuracy was determined by the expression ID = (5-DFS-6-DFS)/2, which represents deviation of the mini-implant`s final position regarding the central point initially selected. Then SW, ID, and screw diameter (SO) were combined to estimate the surgical risk with RI expressed by RI = SO/SW-ID. Results: The 5-DFS and 6-DFS distances were not significantly different. The ID of the G-RSG was 0.17 mm. The low ID ensured a safe RI (<1) in spite of the restricted SW. Conclusions: The G-RSG accuracy allowed fine prediction of the final DFS position in the inter-radicular septum, with a low RI, which is a helpful tool to estimate surgical risks. (Am J Orthod Dentofacial Orthop 2009; 136: 722-35)

Turbulence in collisionless plasmas: statistical analysis from numerical simulations with pressure anisotropy

In recent years, we have experienced increasing interest in the understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments (e. g. the intracluster medium (ICM)) containing magnetic fields that are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions, a new class of kinetic instabilities arises, such as firehose and mirror instabilities, which have been studied extensively in the literature. Their role in the turbulence evolution and cascade process in the presence of pressure anisotropy, however, is still unclear. In this work, we present the first statistical analysis of turbulence in collisionless plasmas using three-dimensional numerical simulations and solving double-isothermal magnetohydrodynamic equations with the Chew-Goldberger-Low laws closure (CGL-MHD). We study models with different initial conditions to account for the firehose and mirror instabilities and to obtain different turbulent regimes. We found that the CGL-MHD subsonic and supersonic turbulences show small differences compared to the MHD models in most cases. However, in the regimes of strong kinetic instabilities, the statistics, i.e. the probability distribution functions (PDFs) of density and velocity, are very different. In subsonic models, the instabilities cause an increase in the dispersion of density, while the dispersion of velocity is increased by a large factor in some cases. Moreover, the spectra of density and velocity show increased power at small scales explained by the high growth rate of the instabilities. Finally, we calculated the structure functions of velocity and density fluctuations in the local reference frame defined by the direction of magnetic lines. The results indicate that in some cases the instabilities significantly increase the anisotropy of fluctuations. These results, even though preliminary and restricted to very specific conditions, show that the physical properties of turbulence in collisionless plasmas, as those found in the ICM, may be very different from what has been largely believed.

Hydrodynamical simulations of Galactic fountains - I. Evolution of single fountains

The ejection of the gas out of the disc in late-type galaxies is related to star formation and is due mainly to Type II supernovae. In this paper, we studied in detail the development of the Galactic fountains in order to understand their dynamical evolution and their influence on the redistribution of the freshly delivered metals over the disc. To this aim, we performed a number of 3D hydrodynamical radiative cooling simulations of the gas in the Milky Way where the whole Galaxy structure, the Galactic differential rotation and the supernova explosions generated by a single OB association are considered. A typical fountain powered by 100 Type II supernovae may eject material up to similar to 2 kpc which than collapses back mostly in the form of dense, cold clouds and filaments. The majority of the gas lifted up by the fountains falls back on the disc remaining within a radial distance Delta R = 0.5 kpc from the place where the fountain originated. This localized circulation of disc gas does not influence the radial chemical gradients on large scale, as required by the chemical models of the Milky Way which reproduce the metallicity distribution without invoking large fluxes of metals. Simulations of multiple fountains fuelled by Type II supernovae of different OB associations will be presented in a companion paper.

DIFFUSION OF MAGNETIC FIELD AND REMOVAL OF MAGNETIC FLUX FROM CLOUDS VIA TURBULENT RECONNECTION

The diffusion of astrophysical magnetic fields in conducting fluids in the presence of turbulence depends on whether magnetic fields can change their topology via reconnection in highly conducting media. Recent progress in understanding fast magnetic reconnection in the presence of turbulence reassures that the magnetic field behavior in computer simulations and turbulent astrophysical environments is similar, as far as magnetic reconnection is concerned. This makes it meaningful to perform MHD simulations of turbulent flows in order to understand the diffusion of magnetic field in astrophysical environments. Our studies of magnetic field diffusion in turbulent medium reveal interesting new phenomena. First of all, our three-dimensional MHD simulations initiated with anti-correlating magnetic field and gaseous density exhibit at later times a de-correlation of the magnetic field and density, which corresponds well to the observations of the interstellar media. While earlier studies stressed the role of either ambipolar diffusion or time-dependent turbulent fluctuations for de-correlating magnetic field and density, we get the effect of permanent de-correlation with one fluid code, i.e., without invoking ambipolar diffusion. In addition, in the presence of gravity and turbulence, our three-dimensional simulations show the decrease of the magnetic flux-to-mass ratio as the gaseous density at the center of the gravitational potential increases. We observe this effect both in the situations when we start with equilibrium distributions of gas and magnetic field and when we follow the evolution of collapsing dynamically unstable configurations. Thus, the process of turbulent magnetic field removal should be applicable both to quasi-static subcritical molecular clouds and cores and violently collapsing supercritical entities. The increase of the gravitational potential as well as the magnetization of the gas increases the segregation of the mass and magnetic flux in the saturated final state of the simulations, supporting the notion that the reconnection-enabled diffusivity relaxes the magnetic field + gas system in the gravitational field to its minimal energy state. This effect is expected to play an important role in star formation, from its initial stages of concentrating interstellar gas to the final stages of the accretion to the forming protostar. In addition, we benchmark our codes by studying the heat transfer in magnetized compressible fluids and confirm the high rates of turbulent advection of heat obtained in an earlier study.

Hydrodynamical simulations of Galactic fountains - II. Evolution of multiple fountains

The ejection of gas out of the disc in late-type galaxies is related to star formation and is mainly due to the explosion of Type II supernovae (SN II). In a previous paper, we considered the evolution of a single Galactic fountain, that is, a fountain powered by a single SN cluster. Using three-dimensional hydrodynamical simulations, we studied in detail the fountain flow and its dependence with several factors, such as the Galactic rotation, the distance to the Galactic centre and the presence of a hot gaseous halo. As a natural followup, this paper investigates the dynamical evolution of multiple generations of fountains generated by similar to 100 OB associations. We have considered the observed size-frequency distribution of young stellar clusters within the Galaxy in order to appropriately fuel the multiple fountains in our simulations. Most of the results of the previous paper have been confirmed, like for example the formation of intermediate velocity clouds above the disc by the multiple fountains. Also, this work confirms the localized nature of the fountain flows: the freshly ejected metals tend to fall back close to the same Galactocentric region where they are delivered. Therefore, the fountains do not change significantly the radial profile of the disc chemical abundance. The multiple fountain simulations also allowed us to consistently calculate the feedback of the star formation on the halo gas. We found that the hot gas gains about 10 per cent of all the SN II energy produced in the disc. Thus, the SN feedback more than compensate for the halo radiative losses and allow for a quasi steady-state disc-halo circulation to exist. Finally, we have also considered the possibility of mass infall from the intergalactic medium and its interaction with the clouds that are formed by the fountains. Though our simulations are not suitable to reproduce the slow rotational pattern that is typically observed in the haloes around the disc galaxies, they indicate that the presence of an external gas infall may help to slow down the rotation of the gas in the clouds and thus the amount of angular momentum that they transfer to the coronal gas, as previously suggested in the literature.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS: THE MAGNETIC FIELD GEOMETRY AND THE INFLUENCE OF THE WIND ON GIANT PLANET MIGRATION

By means of numerical simulations, we investigate magnetized stellar winds of pre-main-sequence stars. In particular, we analyze under which circumstances these stars will present elongated magnetic features (e.g., helmet streamers, slingshot prominences, etc). We focus on weak-lined T Tauri stars, as the presence of the tenuous accretion disk is not expected to have strong influence on the structure of the stellar wind. We show that the plasma-beta parameter (the ratio of thermal to magnetic energy densities) is a decisive factor in defining the magnetic configuration of the stellar wind. Using initial parameters within the observed range for these stars, we show that the coronal magnetic field configuration can vary between a dipole-like configuration and a configuration with strong collimated polar lines and closed streamers at the equator (multicomponent configuration for the magnetic field). We show that elongated magnetic features will only be present if the plasma-beta parameter at the coronal base is beta(0) << 1. Using our self-consistent three-dimensional magnetohydrodynamics model, we estimate for these stellar winds the timescale of planet migration due to drag forces exerted by the stellar wind on a hot-Jupiter. In contrast to the findings of Lovelace et al., who estimated such timescales using the Weber and Davis model, our model suggests that the stellar wind of these multicomponent coronae are not expected to have significant influence on hot-Jupiters migration. Further simulations are necessary to investigate this result under more intense surface magnetic field strengths (similar to 2-3 kG) and higher coronal base densities, as well as in a tilted stellar magnetosphere.

Secondary instabilities in the flow around two circular cylinders in tandem

Direct stability analysis and numerical simulations have been employed to identify and characterize secondary instabilities in the wake of the flow around two identical circular cylinders in tandem arrangements. The centre-to-centre separation was varied from 1.2 to 10 cylinder diameters. Four distinct regimes were identified and salient cases chosen to represent the different scenarios observed, and for each configuration detailed results are presented and compared to those obtained for a flow around an isolated cylinder. It was observed that the early stages of the wake transition changes significantly if the separation is smaller than the drag inversion spacing. The onset of the three-dimensional instabilities were calculated and the unstable modes are fully described. In addition, we assessed the nonlinear character of the bifurcations and physical mechanisms are proposed to explain the instabilities. The dependence of the critical Reynolds number on the centre-to-centre separation is also discussed.

Standard Values for Real-Time Transthoracic Three-Dimensional Echocardiographic Dyssynchrony Indexes in a Normal Population

Background: There is a paucity of information describing the real-time 3-dimensional echocardiography (RT3DE) and dyssynchrony indexes (DIs) of a normal population. We evaluate the RT3DE DIs in a population with normal electrocardiograms and 2- and 3-dimensional echocardiographic analyses. This information is relevant for cardiac resynchronization therapy. Methods: We evaluated 131 healthy volunteers (73 were male, aged 46 +/- 14 years) who were referred for routine echocardiography; who presented normal cardiac structure on electrocardiography, 2-dimensional echocardiography, and RT3DE; and who had no history of cardiac diseases. We analyzed 3-dimensional left ventricular ejection fraction, left ventricle end-diastolic volume, left ventricle end-systolic volume, and left ventricular systolic DI% (6-, 12-, and 16-segment models). RT3DE data were analyzed by quantifying the statistical distribution (mean, median, standard deviation [SD], relative SD, coefficient of skewness, coefficient of kurtosis, Kolmogorov-Smirnov test, D`Agostino-Pearson test, percentiles, and 95% confidence interval). Results: Left ventricular ejection fraction ranged from 50% to 80% (66.1% +/- 7.1%); left ventricle end-diastolic volume ranged from 39.8 to 145 mL (79.1 +/- 24.9 mL); left ventricle end-systolic volume ranged from 12.9 to 66 mL (27 +/- 12.1 mL); 6-segment DI% ranged from 0.20% to 3.80% (1.21% +/- 0.66%), median: 1.06, relative SD: 0.5482, coefficient of skewness: 1.2620 (P < .0001), coefficient of Kurtosis: 1.9956 (P = .0039); percentile 2.5%: 0.2900, percentile 97.5%: 2.8300; 12-segment DI% ranged from 0.22% to 4.01% (1.29% +/- 0.71%), median: 1.14, relative SD: 0.95, coefficient of skewness: 1.1089 (P < .0001), coefficient of Kurtosis: 1.6372 (P = .0100), percentile 2.5%: 0.2850, percentile 97.5%: 3.0700; and 16-segment DI% ranged from 0.29% to 4.88% (1.59 +/- 0.99), median: 1.39, relative SD: 0.56, coefficient of skewness: 1.0792 (P < .0001), coefficient of Kurtosis: 0.9248 (P = .07), percentile 2.5%: 0.3750, percentile 97.5%: 3.750. Conclusion: This study allows for the quantification of RT3DE DIs in normal subjects, providing a comparison for patients with heart failure who may be candidates for cardiac resynchronization therapy. (J Am Soc Echocardiogr 2008; 21: 1229-1235)

Three-dimensional sonographic measurement of contralateral lung volume in fetuses with isolated congenital diaphragmatic hernia

Purpose. To use 3-dimensional sonography (3DUS) to measure contralateral lung volume and evaluate the potential of this measurement to predict neonatal outcome in isolated congenital diaphragmatic hernia (CDH). Methods. Between January 2002 and December 2004, the contralateral lung volumes of 39 fetuses with isolated CDH were measured via 3DUS using rotational multiplanar imaging. The observed/expected contralateral fetal lung volume ratios (o/eContFLVR) were compared with the lung/head ratio (LHR), observed/expected total fetal lung volume ratio (o/e-TotFLVR), and postnatal outcome. Results. Contralateral lung volumes are less reduced than total lung volumes in CDH. The bias and precision of 3DUS in estimating contralateral lung volumes were 0.99 cm(3) and 1.11 cm(3), respectively, with absolute limits of agreement ranging from -1.19 cm(3) to + 3.17 cm(3). The o/e-ContFLVR was significantly lower in neonatal death cases (median, 0.49 cm(3); range, 0.22-0.99 cm(3)) than in survival cases (median, 0.58 cm(3); range, 0.42-0.92 cm(3) [p < 0.011). Overall accuracy of the o/e-ContFLVR, o/e-TotFLVR, and LHR in predicting neonatal death were 67.7% (21/31), 80.7% (25/31), and 77.4% (24/31), respectively. Conclusion. Although o/e-ContFLVR can be precisely measured with 3DUS and can be used to predict neonatal death in CDH, it is less accurate than LHR and o/e-TotFLVR for that purpose. (C) 2007 Wiley Periodicals, Inc.